Smokestack

Perform a dimensional analysis of the smoke plume rising out of a smokestack. The relevant physical parameters are the smoke mass flow rate, m, the smoke density, ρs, the ambient air density, ρa, the gravitational acceleration, g, the diameter of the smokestack, D, and the height of the smokestack, h. Choose D, ρa and g as the repeating parameters. Determine a set of dimensionless groups that describe this problem and apply the Buckingham Pi Theorem to express the dimensionless mass flow rate as a function of the other groups.